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Proof step 1 from proof mapped-full-last (conclusion)

m + n < # avol ⊦ mapped-full?(avol[m + n, mapped(buf)], n, m + 1) ↔ # buf = LEB_SIZE ∧ mapped-full?(avol, n, m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
m + n < # avol ⊦ (∀ n0. n ≤ n0 ∧ ¬ n + m < n0 ∧ n0 < # avol → avol[m + n, mapped(buf)][n0].mapped? ∧ # avol[m + n, mapped(buf)][n0].data = LEB_SIZE) ↔ # buf = LEB_SIZE ∧ (∀ n0. n ≤ n0 ∧ n0 < n + m ∧ n0 < # avol → avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE)

Rule argument

Additional information

Used simplifier rules: mapped-full: ⊦ mapped-full?(avol, n, m) ↔ (∀ n0. n ≤ n0 ∧ n0 < n + m ∧ n0 < # avol → avol[n0].mapped? ∧ # avol[n0].data = LEB_SIZE);% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ # avol[n, aleb] = # avol; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)